[SHIN09-git]

Change and mathematical scope

This adds a source-bound independent audit of apoursh's PR6053 at 12385ca in research/schur-rank-attainment/. No discrepancy was found in the reviewed argument or the declared exact checks. The package provides a separate coordinate-minor attainment construction, a complete ternary d=2 census up to exact simultaneous conjugacy, and an independent evaluation of the ordered closed minimum-rank formula. It imports no PR6053 executable code.

The claims retain the field, invertible-pivot, commuting-idempotent and common-deletion hypotheses. This is bounded computational corroboration plus a written argument, not formal-kernel or independent human acceptance. It changes no shared code, selected result, physical supplier or kappa.

Task and overlap

Base: 721c03822c421b7f7fcbb2598993b947c4d88419, priority revision 8. The frozen complex-rank-shape-decoder card is retained with scope explicitly changed to an algebraic side question. The research began from the released question in PR6031; a final live refresh found concurrent PR6053, so the delivered scope is an audit rather than a new-theorem claim.

Exact predecessors are Nick Petalas's #6031 at acc000f4edfa0b0c4a90b505c6e02a4c3572f74c and Krzysztof Wojt's #5128 at 2839d35e58b3285a1992a3ecbae2809ebef7661b. The unchanged PR6053 proof is explicitly pinned and retained. OVERLAP.json preserves both complete research snapshots; publication-time targeted all-state searches found no existing PR for this package. PUBLICATION.md records publication; the bound files' “local-only” wording describes the frozen research checkpoint.

Added value beyond the target's ternary sample is full coverage of all 186,624 raw d=2 F3 input triples using 8,136 verified conjugacy representatives. The coordinate-minor proof preserves the original sector bases and avoids relying on the target's two-block normal form. Our d=3 family differs from the target's samples; we do not claim to subsume all of its coverage.

Validation

CPython 3.12.10, Windows, standard library only. At scientific commit 84b54b893ef0224aa5080abc1afd219222fa99a2, the registered ordinary and optimized replays, mutation checks, committed-byte check, official export check and optimized read-only Git-free export replay all passed. The 22 original files remain byte-identical; publication adds only PUBLICATION.md.

Coverage: 9,381 distinct triples, 9,389 labelled closed-form comparisons, 32,051 literal P,Q witnesses, and 171,259 exhaustive admissible subspace pairs. This includes every binary d=2 triple, every ternary d=2 conjugacy class, all 512 H for one fixed noncommuting binary d=3 pivot pair, and structured rational/prime-field cases at d=1..4. Nine real code mutants and ten fixture/formula controls are rejected as intended. The independent witness checker recomputes idempotence, commutation, prescribed blocks and literal Schur rank.

Reproduce:

python -B scripts/research_package.py --package research/schur-rank-attainment
python -B scripts/check_research_commit.py --package research/schur-rank-attainment

Or from the package, including a Git-free export:

python -I -W error -B verify.py
python -I -O -W error -B verify.py
python -I -W error -B test_mutations.py

No original PR6053 program/886-case replay, full selected-construction replay, Lean/Docker run or complete source-history closure is claimed. Frozen source pins resolve explicitly.

Known base CI blocker: two shared navigation tests fail on the unchanged canonical base; PR6050 addresses them separately. Local scientific checks pass; hosted status is reported independently. No historical package pin is migrated to bypass a failure.

Credit

Prepared for SHIN09-git with substantial OpenAI Codex assistance, Apache-2.0. Credit apoursh for PR6053's concurrent theorem and ordered closed formula; Nick Petalas for PR6031's reductions, lifts and lower bounds; Krzysztof Wojt for PR5128's ordered factorization and realization; retain their predecessor lineage. Separate primary/oracle/checker paths were developed by one assistant, without subagents. “Independent” does not mean independent human review.

Open next questions

The next justified task is to specify one concrete physical header/caller contract and translate an exact witness into its complete paid/productive invoice. The missing caller, native layout, restoration/ownership and cost contract are the blockers. Further undirected matrix sampling alone would not establish a supplier benefit. See TASK.json and README.md.